The Intel 8257 is a 4-channel DMA controller that allows peripheral devices to directly access memory without involving the CPU. It has priority logic to handle requests from peripherals and issues memory addresses for read/write operations. Each channel has programmable address and count registers and can perform read, write, or verify transfers of up to 64kb of data independently. It uses a master/slave mode and rotating or fixed priority schemes to efficiently manage DMA requests and bus access for high-speed data transfers between peripherals and memory.